Power Spectrum Of Fluctuations Research Articles

Power spectral analysis of voltage-gated channels in neurons

This article develops a fundamental insight into the behavior of neuronal membranes, focusing on their responses to stimuli measured with power spectra in the frequency domain. It explores the use of linear and nonlinear (quadratic sinusoidal analysis) approaches to characterize neuronal function. It further delves into the random theory of internal noise of biological neurons and the use of stochastic Markov models to investigate these fluctuations. The text also discusses the origin of conductance noise and compares different power spectra for interpreting this noise. Importantly, it introduces a novel sequential chemical state model, named p2, which is more general than the Hodgkin–Huxley formulation, so that the probability for an ion channel to be open does not imply exponentiation. In particular, it is demonstrated that the p2 (without exponentiation) and n4 (with exponentiation) models can produce similar neuronal responses. A striking relationship is also shown between fluctuation and quadratic power spectra, suggesting that voltage-dependent random mechanisms can have a significant impact on deterministic nonlinear responses, themselves known to have a crucial role in the generation of action potentials in biological neural networks.

PITSZI: Probing Intra-cluster medium Turbulence with Sunyaev-Zel'dovich Imaging. Application to the triple merging cluster MACS J0717.5+3745

Turbulent gas motions are expected to dominate the non-thermal energy budget of the intracluster medium (ICM). The measurement of pressure fluctuations from high angular resolution Sunyaev-Zel'dovich imaging opens a new avenue to study ICM turbulence, complementary to X-ray density fluctuation measures. We developed a methodological framework designed to optimally extract information on the ICM pressure fluctuation power spectrum statistics, and publicly released the associated software named PITSZI (Probing ICM Turbulence from Sunyaev-Zel'dovich Imaging). We applied this tool to the New IRAM KIDs Array (NIKA) data of the merging cluster MACS J0717.5+3745 to measure its pressure fluctuation power spectrum at high significance, and to investigate the implications for its non-thermal content. Depending on the choice of the radial pressure model and the details of the applied methodology, we measured an energy injection scale L_ inj ∼ 800 kpc. The power spectrum normalization corresponds to a characteristic amplitude reaching A_ δ P / P (k_ peak ) ∼ 0.4. These results were obtained assuming that the ICM of MACS J0717.5+3745 can be described as pressure fluctuations on top of a single (smooth) halo, and were dominated by systematics due to the choice of the radial pressure model. Using simulations, we determined that fitting a radial model to the data can suppress the observed fluctuations by up to $ ∼ 50$%, while a poorly representative radial model can induce spurious fluctuations, which we also quantified. Assuming standard scaling relations between the pressure fluctuations and turbulence, we find that MACS J0717.5+3745 presents a turbulent velocity dispersion σ_v ∼ 1200 km/s, a kinetic to kinetic plus thermal pressure fraction P_ kin / P_ kin+th ∼ 20%, and we estimate the hydrostatic mass bias to b_ HSE ∼ 0.3-0.4. Our results are in excellent agreement with alternative measurements obtained from X-ray surface brightness fluctuations, and in agreement with the fluctuations being adiabatic in nature.

The power spectrum of luminosity distance fluctuations in General Relativity

At low redshift, it is possible to combine spectroscopic information of galaxies with their luminosity or angular diameter distance to directly measure the projection of peculiar velocities (PV) along the line-of-sight. A PV survey probing a large fraction of the sky is subject to so-called wide-angle effects, arising from the variation of the line-of-sight across the sky, and other sub-leading projection effects due to the propagation of the photons in a perturbed cosmological background. In this work, for the first time, we provide a complete description, within linear theory and General Relativity, of the power spectrum of luminosity distance fluctuations, clarifying its relation to the observables in a PV survey. We find that wide-angle effects will be detected at high significance by future observations and will have to be included in the cosmological analysis. Other relativistic projections effects could also be detected provided accurate, per object, distances are available.

Forecasting Constraints from Surface Brightness Fluctuations in Galaxy Clusters

Studies of surface brightness (SB) fluctuations in the intracluster medium present an indirect estimate of turbulent pressure support and associated Mach numbers. While high-resolution X-ray spectroscopy can directly constrain line-of-sight gas motions, including those due to turbulence, such observations are relatively expensive and will be limited to nearby, bright clusters. In this respect, SB fluctuations are the most economical means to constrain turbulent motions at large cluster radii across a range of redshifts and masses. To forecast what current and future X-ray and Sunyaev–Zel’dovich facilities may achieve in SB fluctuation studies, I review and synthesize matters of accuracy and precision with respect to calculating power spectra of SB fluctuations, from which turbulent properties are derived. Balancing concerns of power spectrum accuracy and precision across a range of spatial scales, I propose the use of three annuli with [0, 0.4]R 500, [0.4, 1]R 500, and [1, 1.5]R 500. Adopting these three regions, I calculate the uncertainty in the hydrostatic mass bias, σbM , that can be achieved for various instruments in several scenarios. I find that Lynx and AtLAST are competitive in their constraints at R 500, while AtLAST should perform better when constraining σbM at R 200.

Global Analysis of the Extended Decreases in Cosmic Rays Observed with Worldwide Networks of Neutron Monitors and Muon Detectors: Temporal Variation of the Rigidity Spectrum and Its Implication

This paper presents the global analysis of two extended decreases in the galactic cosmic-ray intensity observed by worldwide networks of ground-based detectors in 2012. This analysis is capable of separately deriving the cosmic-ray density (or omnidirectional intensity) and anisotropy, each as a function of time and rigidity. A simple diffusion model along the spiral field line between Earth and a cosmic-ray barrier indicates the long duration of these events, resulting from about 190° eastern extent of a barrier such as an interplanetary shock followed by the sheath region and/or the corotating interaction region (CIR). It is suggested that the coronal mass ejection merging with and compressing the preexisting CIR at its flank can produce such an extended barrier. The derived rigidity spectra of the density and anisotropy both vary in time during each event period. In particular we find that the temporal feature of the “phantom Forbush decrease (FD)” reported in an analyzed period is dependent on rigidity, and looks quite different at different rigidities. From these rigidity spectra of the density and anisotropy, we derive the rigidity spectrum of the average parallel mean free path of pitch angle scattering along the spiral field line and infer the power spectrum of the magnetic fluctuation and its temporal variation. The possible physical cause of the strong rigidity dependence of the phantom FD is also discussed. These results demonstrate the high-energy cosmic rays observed at Earth responding to remote space weather.

Spectral properties of solar wind plasma flux and magnetic field fluctuations across fast reverse interplanetary shocks

We have analyzed spectra of fluctuations in the solar wind plasma flux and the magnetic field magnitude near the front of a fast reverse shocks, using data from the BMSW device (Bright Monitor of Solar Wind) operating on the SPEKTR-R satellite. Its time resolution made it possible to study plasma flux fluctuations up to a frequency of 16 Hz. Magnetic field data was taken mainly from the WIND satellite, for which the frequency of the fluctuations considered was up to 5.5 Hz. The slope of the spectra of the solar wind flux fluctuations on MHD scales has been shown to be close to the slope of the spectrum of magnetic field fluctuations in the disturbed region. On kinetic scales, the difference can be significant. For the region ahead of the front, the difference in the slope of the spectrum can be quite large both in the MHD and in the kinetic region. The frequency of the break of the flux spectrum ranges from 0.6 to 1.3 Hz, which corresponds to the scale of the proton inertial length. In a number of events, however, the shape of the spectrum indicates the influence of the proton gyroradius frequency, which is usually 0.05–0.15 Hz. The break in the power spectrum of magnetic field fluctuations also more often ranges from 0.7 to 1.2 Hz. In this case, the slope of the MHD part of the spectrum changes little, but in the kinetic part it increases slightly when moving to the disturbed region.

Анализ спектров флуктуаций величины потока плазмы и модуля магнитного поля на обратных ударных волнах

We have analyzed spectra of fluctuations in the solar wind plasma flux and the magnetic field magnitude near the front of a fast reverse shocks, using data from the BMSW device (Bright Monitor of Solar Wind) operating on the SPEKTR-R satellite. Its time resolution made it possible to study plasma flux fluctuations up to a frequency of 16 Hz. Magnetic field data was taken mainly from the WIND satellite, for which the frequency of the fluctuations considered was up to 5.5 Hz. The slope of the spectra of the solar wind flux fluctuations on MHD scales has been shown to be close to the slope of the spectrum of magnetic field fluctuations in the disturbed region. On kinetic scales, the difference can be significant. For the region ahead of the front, the difference in the slope of the spectrum can be quite large both in the MHD and in the kinetic region. The frequency of the break of the flux spectrum ranges from 0.6 to 1.3 Hz, which corresponds to the scale of the proton inertial length. In a number of events, however, the shape of the spectrum indicates the influence of the proton gyroradius frequency, which is usually 0.05–0.15 Hz. The break in the power spectrum of magnetic field fluctuations also more often ranges from 0.7 to 1.2 Hz. In this case, the slope of the MHD part of the spectrum changes little, but in the kinetic part it increases slightly when moving to the disturbed region.

1/fα noise in the Robin Hood model

Abstract We consider the Robin Hood dynamics, a one-dimensional extremal self-organized critical model that describes the low-temperature creep phenomenon. One of the key quantities is the time evolution of the state variable (force noise). To understand the temporal correlations, we compute the power spectra of the local force fluctuations and apply finite-size scaling to get scaling functions and critical exponents. We find a signature of the 1 / f α noise for the local force with a nontrivial value of the spectral exponent 0 < α < 2 . We also examine temporal fluctuations in the position of the extremal site and a local activity signal. We present results for different local interaction rules of the model.

Detecting relativistic Doppler by multi-tracing a single galaxy population

New data from ongoing galaxy surveys, such as the Euclid satellite and the Dark Energy Spectroscopic Instrument (DESI), are expected to unveil physics on the largest scales of our universe. Dramatically affected by cosmic variance, these scales are of interest to large-scale structure studies as they exhibit relevant corrections due to general relativity (GR) in the n-point statistics of cosmological random fields. We focus on the relativistic, sample-dependent Doppler contribution to the observed clustering of galaxies, whose detection will further confirm the validity of GR in cosmological regimes. Sample- and scale-dependent, the Doppler term is more likely to be detected via cross-correlation measurements, where it acts as an imaginary correction to the power spectrum of fluctuations in galaxy number counts. We present a method allowing us to exploit multi-tracer benefits from a single data set, by subdividing a galaxy population into two sub-samples, according to galaxies’ luminosity/magnitude. To overcome cosmic variance we rely on a multi-tracer approach, and to maximise the detectability of the relativistic Doppler contribution in the data, we optimise sample selection. As a result, we find the optimal split and forecast the relativistic Doppler detection significance for both a DESI-like Bright Galaxy Sample and a Euclid-like Hα galaxy population.

The cosmological collider in R 2 inflation

Starobinsky's R 2 inflation manifests a best-fit scenario for the power spectrum of primordial density fluctuations. Observables derived from the slow-roll picture of the R 2 model in the Einstein frame relies on the conformal transformation of the metric, which inevitably induces a unique exponential-type couplings of the rolling scalaron with all matter fields during inflation. The “large-field” nature of the R 2 model further invokes non-negligible time and scale dependence to the matter sector through such an exponential coupling, modifying not only the dynamics of matter perturbations on superhorizon scales but also their decay rates. In this work, we identify the simplest observable of the cosmological collider physics built in the background of R 2 inflation, focusing on the so-called “quantum primordial clock” signals created by the non-local propagation of massive scalar perturbations. Our numerical formalism based on the unique conformal coupling can have extended applications to (quasi-)single-field inflationary models with non-trivial couplings to gravity or models that originated from the f(R) modification of gravity.

Surface Brightness Fluctuations in Two SPT Clusters: A Pilot Study

Studies of surface brightness fluctuations in the intracluster medium present an indirect probe of turbulent properties such as the turbulent velocities, injection scales, and the slope of the power spectrum of fluctuations toward smaller scales. With the advancement of Sunyaev–Zel’dovich (SZ) studies and surveys relative to X-ray observations, we seek to investigate surface brightness fluctuations in a sample of South Pole Telescope (SPT)-SZ clusters which also have archival XMM-Newton data. Here we present a pilot study of two typical clusters in that sample: SPT-CLJ0232-4421 and SPT-CLJ0638-5358. We infer injection scales larger than 500 kpc in both clusters and Mach numbers ≈ 0.5 in SPT-CLJ0232-4421 and Mach numbers ≈ 0.6–1.6 in SPT-CLJ0638-5358, which has a known shock. We find hydrostatic bias values for M 500 less than 0.2 for SPT-CLJ0232-4421 and less than 0.1 for SPT-CLJ0638-5358. These results show the importance to assess quantitative values via a detailed multiwavelength approach and suggest that the drivers of turbulence may occur at quite large scales.

Cosmological perturbations from five-dimensional inflation

It was recently proposed that five-dimensional inflation can relate the causal size of the observable universe to the present weakness of gravitational interactions by blowing up an extra compact dimension from the microscopic fundamental length of gravity to a large size in the micron range, as required in the Dark Dimension proposal. Here, we compute the power spectrum of all primordial fluctuations emerging from a 5-dimensional inflaton in a slow-roll region of its potential, showing an interesting change of behaviour at large scales corresponding to angles larger than about 10 degrees in the sky.

Phase transition in the noise power spectrum of interacting-spin fluctuations at infinite temperature

Phase transition in the noise power spectrum of interacting-spin fluctuations at infinite temperature

Transient RFI environment of LOFAR-LBA at 72–75 MHz

Context. Measurement of the highly redshifted and faint 21-cm signal of neutral hydrogen from the Cosmic Dawn and Epoch of Reionisation promises to unveil a wealth of information about the astrophysical processes that governed the structure formation and evolution of the universe during the first billion years of its evolution. Aims. The AARTFAAC Cosmic Explorer (ACE) program utilises the AARTFAAC wide-field imager of LOFAR to measure the power spectrum of the intensity fluctuations of the redshifted 21-cm signal from the Cosmic Dawn at z ∼ 18 corresponding to the global 21-cm absorption feature reported by the EDGES experiment. Radio frequency interference (RFI) from various sources, such as aeroplane communication, contaminates the observed data and it is crucial to exclude the RFI-affected data in the analysis for any reliable detection. In this work, we solely focus on investigating the impact of non-ground-based transient RFI on the analysis of ACE observations. Methods. We use cross-power spectra and cross-coherence metrics to assess the correlation of RFI over time and investigate the level of impact of transient RFI on the 21-cm signal power spectrum estimation. Results. We detected moving sky-based transient RFI sources that cross the field of view within a few minutes and appear to be mainly from aeroplane communication beacons at the location of the LOFAR core in the 72−75 MHz band (a part of the EDGES absorption trough), by inspecting filtered images. We find that this transient RFI is mostly uncorrelated over time and is only expected to dominate over the thermal noise for an extremely deep integration time of 3000 h or more with a hypothetical instrument that is sky temperature dominated at 75 MHz. We find no visible correlation over different k-modes in Fourier space in the presence of noise for realistic thermal noise scenarios. Conclusions. We conclude that the sky-based transient RFI from aeroplanes, satellites and meteorites at present does not pose a significant concern for the ACE analyses at the current level of sensitivity and after integrating over the available ∼500 h of observed data. However, it is crucial to mitigate or filter such transient RFI for more sensitive experiments aiming for significantly deeper integration.

OLIMPO: A balloon-borne SZE imager to probe ICM dynamics and the WHIM

OLIMPO is a proposed Antarctic balloon-borne Sunyaev-Zel’dovich effect (SZE) imager to study gas dynamics associated with structure formation along with the properties of the warm-hot intergalactic medium (WHIM) residing in the connective filaments. During a 25 day flight OLIMPO will image a total of 10 z∼0.05 galaxy clusters and 8 bridges at 145, 250, 365, and 460 GHz at an angular resolution of 1.0′–3.3′. The maps will be significantly deeper than those planned from CMB-S4 and CCAT-P, and will have excellent fidelity to the large angular scales of our low-z targets, which are difficult to probe from the ground. In combination with X-ray data from eROSITA and XRISM we will transform our current static view of galaxy clusters into a full dynamic picture by measuring the internal intra-cluster medium (ICM) velocity structure with the kinematic SZE, X-ray spectroscopy, and the power spectrum of ICM fluctuations. Radio observations from ASKAP and MeerKAT will be used to better understand the connection between ICM turbulence and shocks with the relativistic plasma. Beyond the cluster boundary, we will combine thermal SZE maps from OLIMPO with X-ray imaging from eROSITA to measure the thermodynamics of the WHIM residing in filaments, providing a better understanding of its properties and its contribution to the total baryon budget.

21-cm Epoch of reionisation power spectrum with closure phase using the Murchison Widefield Array

Abstract The radio interferometric closure phases can be a valuable tool for studying cosmological HI from the early Universe. Closure phases have the advantage of being immune to element-based gains and associated calibration errors. Thus, calibration and errors therein, which are often sources of systematics limiting standard visibility-based approaches, can be avoided altogether in closure phase analysis. In this work, we present the first results of the closure phase power spectrum of HI 21-cm fluctuations using the Murchison Widefield Array (MWA), with $\sim12$ h of MWA phase II observations centred around redshift, $z\approx 6.79$ , during the Epoch of Reionisation. On analysing three redundant classes of baselines – 14, 24, and 28 m equilateral triads, our estimates of the $2\sigma$ (95% confidence interval) 21-cm power spectra are $\lesssim(184)^2 pseudo\,\mathrm{mK}^2$ at ${k}_{||} = 0.36 pseudo\ h \mathrm{Mpc}^{-1}$ in the EoR1 field for the 14 m baseline triads, and $\lesssim(188)^2 pseudo\,\mathrm{mK}^2$ at $k_{||} = 0.18 \,pseudo\ h \mathrm{Mpc}^{-1}$ in the EoR0 field for the 24 m baseline triads. The ‘pseudo’ units denote that the length scale and brightness temperature should be interpreted as close approximations. Our best estimates are still 3-4 orders high compared to the fiducial 21-cm power spectrum; however, our approach provides promising estimates of the power spectra even with a small amount of data. These data-limited estimates can be further improved if more datasets are included into the analysis. The evidence for excess noise has a possible origin in baseline-dependent systematics in the MWA data that will require careful baseline-based strategies to mitigate, even in standard visibility-based approaches.

Physical consistency and invariance in machine learning of turbulent signals

This paper concerns an investigation of the invariance and consistency of deep learning of turbulent pressure fluctuations. The long-short-memory model is employed to predict wall pressure fluctuations across physical regimes featuring turbulence, shock–boundary layer interaction, and separation. The model's sensitivity to the data inputs is examined using different input data sets. Training the deep learning model based on the raw signals from different flow regions leads to large inaccuracies. It is shown that the data must be appropriately pre-processed before training for the deep learning model predictions to become consistent. Removing the mean and using the normalized fluctuating component of the signal, the deep learning predictions not only greatly improved in accuracy but, most importantly, converged and became consistent, provided that the signal sparsity remains within the inertial sub-range of the turbulence energy spectrum cascade. The power spectra of the surface pressure fluctuations reveal that the model provides high accuracy up to a certain frequency for the fully turbulent flow. The deep learning model's consistency is evidenced by being transferable across the various probe positions on the wall despite the significant differences in the turbulent flow properties in the training data set, i.e., signals obtained before, after, and inside the shock–boundary layer interaction regions. The model's prediction consistency and invariance to the turbulent signal training location(s) are promising for applying deep learning models to various turbulent flows.

Particle acceleration by sub-proton cyclotron frequency spectrum of dispersive Alfven waves in inhomogeneous solar coronal plasmas

ABSTRACT The problem of explaining observed soft X-ray fluxes during solar flares, which invokes acceleration of large fraction of electrons, if the acceleration takes places at the solar coronal loop-top, can potentially be solved by postulating that flare at loop-top creates dispersive Alfven waves (DAWs) which propagate towards the foot-points. As DAWs move in progressively denser parts of the loop (due to gravitational stratification) the large fraction of electrons is no longer needed. Here, we extend our previous results by considering f−1 frequency spectrum of DAWs and add He++ ions using fully kinetic particle-in-cell (PIC) simulations. We consider cases when transverse density gradient is in the range 4–40c/ωpe and DAW driving frequency is 0.3–0.6ωcp. We find that (i) The frequency spectrum case does not affect electron acceleration fraction in the like-to-like cases, but few times larger percentage of He++ heating is seen due to ion cyclotron resonance; (ii) In cases when counter propagating DAWs collide multiple-times, much larger electron and ion acceleration fractions are found, but the process is intermittent in time. This is because intensive heating (temperature increase) makes the-above-thermal-fraction smaller; Also more isotropic velocity distributions are seen; (iii) Development of kink oscillations occurs when DAWs collide; (iv) Scaling of the magnetic fluctuations power spectrum steepening in the higher-density regions is seen, due to wave refraction. Our PIC runs produce much steeper slopes than the orginal spectrum, indicating that the electron-scale physics has a notable effect on DAW spectrum evolution.

Gravity Wave Characterization of Multiple Convections in the Beijing–Tianjin–Hebei Region

Using high-precision microbarograph data and radar data to analyze the gravity fluctuation characteristics of four convective processes of different intensities that occurred in the Beijing–Tianjin–Hebei region in June 2018, the results show that convective cases are accompanied by gravity fluctuations of different time scales and can be separated from the background field through the wavelet transform. The stronger the convective process, the larger the fluctuation amplitude. As the convection gradually approaches the station, the fluctuation frequency broadens, and smaller period fluctuations are excited. Through Fourier analysis, the longer period of fluctuation is concentrated at about 190 min, and the power spectrum of the short-period fluctuation is weak, with a peak frequency of about 2.04 × 10−4 Hz. The results obtained by wavelet transform are similar to them, but they reflect the characteristics of fluctuation evolution over time: (1) convection-related gravity wave periods are mainly concentrated in three bands: 15–40 min, 40–120 min, and 120–250 min; (2) there may be precursor activity before the occurrence of the convective flow, and the long-period fluctuation occurs about 1–4 h ahead of time; (3) there is a short-period fluctuation in the process of convective system development, and the period range is mainly concentrated at about 40–120 min; strong convective clouds may inspire shorter-period fluctuations. The geometrical relationship between the microbarograph stations shows that the short-period fluctuations of the four convective cases propagate at a speed of 14–37 m/s, and the azimuthal angle is consistent with the convective orientation, which indicates that there is a close relationship between gravity waves and convection.

Turbulence Properties of Interplanetary Coronal Mass Ejections in the Inner Heliosphere: Dependence on Proton Beta and Flux Rope Structure

Interplanetary coronal mass ejections (ICMEs) have low proton beta across a broad range of heliocentric distances and a magnetic flux rope structure at large scales, making them a unique environment for studying solar wind fluctuations. Power spectra of magnetic field fluctuations in 28 ICMEs observed between 0.25 and 0.95 au by Solar Orbiter and Parker Solar Probe have been examined. At large scales, the spectra were dominated by power contained in the flux ropes. Subtraction of the background flux rope fields increased the mean spectral index from −5/3 to −3/2 at kd i ≤ 10−3. Rope subtraction also revealed shorter correlation lengths in the magnetic field. The spectral index was typically near −5/3 in the inertial range at all radial distances regardless of rope subtraction and steepened to values consistently below −3 with transition to kinetic scales. The high-frequency break point terminating the inertial range evolved approximately linearly with radial distance and was closer in scale to the proton inertial length than the proton gyroscale, as expected for plasma at low proton beta. Magnetic compressibility at inertial scales did not show any significant correlation with radial distance, in contrast to the solar wind generally. In ICMEs, the distinctive spectral properties at injection scales appear mostly determined by the global flux rope structure while transition-kinetic properties are more influenced by the low proton beta; the intervening inertial range appears independent of both ICME features, indicative of a system-independent scaling of the turbulence.